Dynamic stabilization of ablative Rayleigh-Taylor instability in the presence of a temporally modulated laser pulse

This paper presents a numeric study of the dynamic stabilization of the ablative Rayleigh-Taylor instability (ARTI) in the presence of a temporally modulated laser pulse. The results show that the specially modulated laser produces a dynamically stabilized configuration near the ablation front. The physical features of the relevant laser-driven parameters in the unperturbed ablative flows have been analyzed to reveal the inherent stability mechanism underlying the dynamically stabilized configuration. A single-mode ARTI for the modulated laser pulse is first compared with that of the unmodulated laser pulse. The results show that the modulated laser stabilizes the surface perturbations and reduces the linear growth rate and enhancement of the cutoff wavelength. For multimode perturbations, the dynamic stabilization effect of the modulated laser pulse contributes to suppress the small-scale structure and reduce the width of the mixing layer. Moreover, the results show that the stabilization effect of the modulated laser pulse decreases as the maximum wavelength increases.

Figure 1

(a) Schematic of planar target. (b) Profile of laser intensity. (c) Distribution of initial basic flow ($t$ = 0.0 ns) along the $x$ axis. The minimum density gradient scale length of the ablation front is about 0.93 $\mu \mathrm{m}$.

Figure 2

Laser intensity profiles for unmodulated (dashed line) and for specially modulated (solid line) pulse shapes. A constant intensity of the unmodulated laser pulse as a reference case is always $3.0\times {10}^{14}$ W/${\mathrm{cm}}^2$. The specially modulated case of $50\%$ modulation depth consists of a symmetric square wave with a period of 2.0 ns, the peak intensity of $4.5\times {10}^{14}$ W/${\mathrm{cm}}^2$, and the valley intensity of $1.5\times {10}^{14}$ W/${\mathrm{cm}}^2$.

Figure 3

Temporal evolution of the interesting laser-driven parameters in two unperturbed ablative flows for modulated (solid line) and unmodulated (dashed line) laser pulses. The laser parameters include (a) position $s$, (b) acceleration $g$, (c) pressure $p_a$ of the ablation front (defined as the zone at half-peak density), (d) peak density ${\rho }_h$, (e) mass ablation rate $\dot{m}$, and (f) ablation velocity $V_a$.

Figure 4

Evolution of the adiabat near the ablation front for the modulated (solid line) laser pulse compared with that of the unmodulated (dashed line) laser pulse. The dotted line shows the average adiabat of the modulated laser pulse.

Figure 5

Spatial profiles of density (solid lines) and pressure (dashed lines) near the ablation front for unmodulated (top row) and modulated (bottom row) laser pulses at 2.8 ns [(a) and (c)] and 3.5 ns [(b) and (d)]. The interface for the unmodulated laser pulse is always unstable because the pressure gradient opposes the density gradient. The interfaces for the modulated laser pulse at 2.8 ns and 3.5 ns are unstable and stable, respectively.

Figure 6

Density contours of the single-mode ARTI initiated by a small-amplitude perturbation for unmodulated (top row) and modulated (bottom row) laser pulses at 2.0, 4.0, 6.0, and 8.0 ns. The initial wavelength and its perturbation amplitude are $\lambda =60 \mu \mathrm{m}$ and $A_0\simeq 0.0034\lambda$, respectively.

Figure 7

Evolution of normalized bubble-spike amplitudes (${\eta }_{b+s}/\lambda$) of the single-mode ARTI driven by the unmodulated (dashed lines) and modulated (solid lines) laser pulses for a perturbation with (a) $\lambda =20 \mu \mathrm{m}$, (b) 60 $\mu \mathrm{m}$, and (c) 90 $\mu \mathrm{m}$. The initial perturbation amplitudes for cases (a)–(c) are about 0.083, 0.206, and 0.323 $\mu \mathrm{m}$, respectively.

Figure 8

(a) Temporal evolution of driving accelerations obtained from unmodulated (dashed line) and modulated (solid line) laser pulses. The dotted line represents an asymmetric square-wave modulation of the oscillatory acceleration. (b) Linear growth rates obtained from numerical simulations with unmodulated (diamonds) and modulated (spheres) laser pulses, Lindl formula (dashed line) [17], Betti theory [38], and the Piriz model (dashed line) [39, 40]. The cutoff wavelengths of the numerical simulations for the unmodulated and modulated laser pulses are about 5.0 and 20.0 $\mu \mathrm{m}$, respectively.

Figure 9

Density contours of initial multimode ARTI for unmodulated laser pulse at times (a) 2.0 ns, (b) 4.0 ns, (c) 6.0 ns, and (d) 8.0 ns. The maximum initial wavelength and its perturbation amplitude are ${\lambda }_3$ = 50 $\mu \mathrm{m}$ and $A_{3,0}\simeq 0.552 \mu \mathrm{m}$.

Figure 10

Density contours of initial multimode ARTI for modulated laser pulse at times (a) 2.0 ns, (b) 4.0 ns, (c) 6.0 ns, and (d) 8.0 ns. The maximum initial wavelength and its perturbation amplitude are the same as in Fig. 9.

Figure 11

Comparison of Fourier amplitude distributions as a function of mode number at (a) 2.0 ns, (b) 4.0 ns, and (c) 6.0 ns, converted in the areal density and irradiated by unmodulated laser pulses (diamonds) and modulated laser pulses (spheres).

Figure 12

Evolution of mixing layer widths for unmodulated (dashed lines) and modulated (solid lines) laser pulses for simulation domains (a) $L_y=150 \mu \mathrm{m}$, (b) $L_y=240 \mu \mathrm{m}$, and (c) $L_y=360 \mu \mathrm{m}$ in the $y$ direction. The maximum initial wavelengths (i.e., the perturbation amplitudes) for three cases (a)–(c) are 50 $\mu \mathrm{m}$ ($\sim 0.552 \mu \mathrm{m}$), 80 $\mu \mathrm{m}$ ($\sim 0.858 \mu \mathrm{m}$) and 120 $\mu \mathrm{m}$ ($\sim 1.143 \mu \mathrm{m}$), respectively. The one-dimensional parameters of the unmodulated and modulated pulses are the same as in Figs. 9 and 10.